Calculus

Calculus Peak 2036m Prominence: 531m Located at the head of an unnamed tributary of Swallop Creek. The peak is in an icredibly steep and rocky terrain, with every slope at the limit of possible steepness. Calculus is the branch of mathematics that deals with limits and rates of change. Calculus is one of the most important breakthroughs in modern mathematics, answering questions that had puzzled mathematicians, scientists, and philosophers for more than two thousand years. In particular, calculus gave a clear and precise definition of infinity, both in the case of the infinitely large and the infinitely small. It provided an answer to Zenos paradoxes and gave the first clear definition of what Aristotle called the quality of motion. Calculus was not discovered all at once. In the ancient world, Eudoxus and Archimedes proposed mathematical ideas that can now be seen as similar to calculus. In India and Japan mathematicians had ideas that can now be understood as calculus (see History below). In Europe, Wallis, Barrow, and James Gregory proposed ideas that would now be considered integrals, derivatives, and the fundamental theorem of calculus. But it is Isaac Newton and Gottfried Leibniz who brought all these ideas together, and they are usually credited with the independent and nearly simultaneous creation of calculus. It was generations after Newton and Leibniz that Cauchy and other mathematicians finally put calculus on a rigorous basis, with the definition of the limit. From a mathematical standpoint, calculus gives the definitions and properties of three linear operators, the limit, the derivative, and the integral.